# Sum of first n term of Series 3, 5, 9, 17, 33….

Given n, we need to find sum of first n terms of the series represented as Sn = 3 + 5 + 9 + 17 + 33 … upto n

Examples:

```Input : 2
Output : 8
3 + 5 = 8

Input : 5
Output : 67
3 + 5 + 9 + 17 + 33 = 67
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Let, the nth term be denoted by tn.
This problem can easily be solved by splitting each term as follows :

Sn = 3 + 5 + 9 + 17 + 33……
Sn = (2+1) + (4+1) + (8+1) + (16+1) +……
Sn = (2+1) + (2*2+1) + (2*2*2+1) + (2*2*2*2+1) +……+ ((2*2*2..unto n times) + 1)

We observed that the nth term can be written in terms of powers of 2 and 1.
Hence, the sum of first n terms is given as follows:

Sn = (2+1) + (4+1) + (8+1) + (16+1) +……+ upto n terms
Sn = (1 + 1 + 1 + 1 + …unto n terms) + (2 + 4 + 8 + 16 + …upto nth power of 2)
In above formula,
2 + 4 + 8 + 16…. is a G.P.
It’s sum of first n terms is given by 2*(2^n-1)/(2-1) = 2^(n+1) – 2 (using G.P. formula)
Sn = n + 2*(2^n – 1)
Sn = 2^(n+1) + n -2

## C++

 `// C++ program to find sum of first n terms ` `#include ` `using` `namespace` `std; ` ` `  `int` `calculateSum(``int` `n) ` `{ ` `    ``// Sn = n*(4*n*n + 6*n - 1)/3 ` `    ``return` `(``pow``(2, n + 1) + n - 2); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// number of terms to be included in sum ` `    ``int` `n = 4; ` ` `  `    ``// find the Sn ` `    ``cout << ``"Sum = "` `<< calculateSum(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find ` `// sum of first n terms ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` `static` `int` `calculateSum(``int` `n) ` `{ ` `    ``// Sn = n*(4*n*n + 6*n - 1)/3 ` `    ``return` `((``int``)Math.pow(``2``, n + ``1``) +  ` `                             ``n - ``2``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``// number of terms to  ` `    ``// be included in sum ` `    ``int` `n = ``4``; ` ` `  `    ``// find the Sn ` `    ``System.out.println(``"Sum = "` `+  ` `                ``calculateSum(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Kirti_Mangal `

## Python

 `# Python program to find sum  ` `# of n terms of the series ` `def` `calculateSum(n): ` ` `  `    ``return` `(``2``*``*``(n ``+` `1``) ``+` `n ``-` `2``) ` ` `  `# Driver Code ` ` `  `# number of terms for the sum ` `n ``=` `4` ` `  `# find the Sn ` `print``(``"Sum ="``, calculateSum(n)) ` ` `  `# This code is contributed  ` `# by Surendra_Gangwar `

## C#

 `//C# program to find ` `// sum of first n terms ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `static` `int` `calculateSum(``int` `n) ` `{ ` `    ``// Sn = n*(4*n*n + 6*n - 1)/3 ` `    ``return` `((``int``)Math.Pow(2, n + 1) +  ` `                            ``n - 2); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``// number of terms to  ` `    ``// be included in sum ` `    ``int` `n = 4; ` ` `  `    ``// find the Sn ` `    ``Console.WriteLine(``"Sum = "` `+  ` `                ``calculateSum(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by inder_verma.. `

## PHP

 ` `

Output:

```Sum = 34
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

5

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.